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I am doing monte carlo simulations. In the first run the experiment is repeated e.g. 10000 times. The result looks like x+/-y, y is the relative error. Next, I change a part of the experiment and run again for e.g. 10000 times and have the result u+/-v, v the relative error.

It is possible that the difference between x and u is small and also there is the relative error. How can I assess this difference with respect to the relative errors?

Example: First result: 91.6 +/- 9.84 Second result: 95.12 +/- 12.33 Is there a “real” difference in the results or is it just something within the errors? Any help is very appreciated. Thanks Ulrich

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A simple strategy is assume a normal distribution for your MC results. Please check if that applies to you, lot's of practical MC applications (at least my own experience) assume normal or log-normal distribution.

Now, you have your assumed distribution and all the individual recorded values. What's stopping you from something like t-test?

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